Cosmic web anisotropy is the primary indicator of halo assembly bias. (arXiv:1903.02007v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Ramakrishnan_S/0/1/0/all/0/1">Sujatha Ramakrishnan</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Paranjape_A/0/1/0/all/0/1">Aseem Paranjape</a> (IUCAA), <a href="http://arxiv.org/find/astro-ph/1/au:+Hahn_O/0/1/0/all/0/1">Oliver Hahn</a> (OCA), <a href="http://arxiv.org/find/astro-ph/1/au:+Sheth_R/0/1/0/all/0/1">Ravi K. Sheth</a> (UPenn/ICTP)

The internal properties of dark matter haloes correlate with the large-scale
halo clustering strength at fixed halo mass $-$ an effect known as assembly
bias $-$ and are also strongly affected by the local, non-linear cosmic web.
Characterising a halo’s local web environment by its tidal anisotropy $alpha$
at scales $sim4$ x the halo radius, we demonstrate that these multi-scale
correlations represent two distinct statistical links: one between the internal
property and $alpha$, and the other between $alpha$ and large-scale (
$>30h^{-1}$Mpc) halo bias $b_1$. We focus on scalar internal properties of
haloes related to formation time (concentration $c_{rm vir}$), shape (mass
ellipsoid asphericity $c/a$), velocity dispersion structure (velocity ellipsoid
asphericity $c_v/a_v$ and velocity anisotropy $beta$) and angular momentum
(dimensionless spin $lambda$) in the mass range $8times10^{11}< M_{rm vir}/(h^{-1}M_odot)<5times10^{14}$. Using conditional correlation coefficients and other detailed tests, we show that the joint distribution of $alpha$, $b_1$ and any of the internal properties $cin{beta,c_v/a_v,c/a,c_{rm vir},lambda}$ is consistent with $p(alpha,b_1,c)simeq p(alpha)p(b_1|alpha)p(c|alpha)$, at all but the largest masses. $textit{Thus, all low-mass assembly bias trends $c-b_1$ reflect the two fundamental correlations $c-alpha$ and $b_1-alpha$.}$ Our results are unaffected by the exclusion of haloes with recent major merger events or splashback objects, although the latter are distinguished by the fact that $alpha$ does not explain their assembly bias trends. The overarching importance of $alpha$ provides a new perspective on the nature of assembly bias of distinct haloes, with potential ramifications for incorporating realistic assembly bias effects into mock catalogs of future large-scale structure surveys and for detecting galaxy assembly bias.

The internal properties of dark matter haloes correlate with the large-scale
halo clustering strength at fixed halo mass $-$ an effect known as assembly
bias $-$ and are also strongly affected by the local, non-linear cosmic web.
Characterising a halo’s local web environment by its tidal anisotropy $alpha$
at scales $sim4$ x the halo radius, we demonstrate that these multi-scale
correlations represent two distinct statistical links: one between the internal
property and $alpha$, and the other between $alpha$ and large-scale (
$>30h^{-1}$Mpc) halo bias $b_1$. We focus on scalar internal properties of
haloes related to formation time (concentration $c_{rm vir}$), shape (mass
ellipsoid asphericity $c/a$), velocity dispersion structure (velocity ellipsoid
asphericity $c_v/a_v$ and velocity anisotropy $beta$) and angular momentum
(dimensionless spin $lambda$) in the mass range $8times10^{11}< M_{rm
vir}/(h^{-1}M_odot)<5times10^{14}$. Using conditional correlation
coefficients and other detailed tests, we show that the joint distribution of
$alpha$, $b_1$ and any of the internal properties
$cin{beta,c_v/a_v,c/a,c_{rm vir},lambda}$ is consistent with
$p(alpha,b_1,c)simeq p(alpha)p(b_1|alpha)p(c|alpha)$, at all but the
largest masses. $textit{Thus, all low-mass assembly bias trends $c-b_1$
reflect the two fundamental correlations $c-alpha$ and $b_1-alpha$.}$ Our
results are unaffected by the exclusion of haloes with recent major merger
events or splashback objects, although the latter are distinguished by the fact
that $alpha$ does not explain their assembly bias trends. The overarching
importance of $alpha$ provides a new perspective on the nature of assembly
bias of distinct haloes, with potential ramifications for incorporating
realistic assembly bias effects into mock catalogs of future large-scale
structure surveys and for detecting galaxy assembly bias.

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